Theory and Algorithm of Estimating Energy Consumption Breakdowns using ON/OFF State Sensing

This article considers a problem of periodically estimating energy consumption breakdowns for main appliances inside building using a single power meter and the knowledge of the ON/OFF states of individual appliances. In the first part of this article, we formulate the problem as a constrained convex optimization problem with tunable parameters. Then we propose an online algorithm that adaptively determines the optimization parameters to robustly estimate the breakdown information. The proposed solution is evaluated by experiment using a scaled-down proof-of-concept prototype with real measurements. In the second part, we provide detailed analysis to understand the performance of our proposed algorithm. We first develop a stochastic model to describe evolution of appliances’ ON/OFF states using continuous-time Markov chain. Then we derive analytical bounds of estimation error and the probability of a rank-deficient binary matrix. Those analytical bounds are verified by extensive simulations. Finally, we study the effect of collinearity of binary data matrix on estimation performance. Simulation results suggest that our algorithm is robust against the collinearity of binary dataset.